The shape of the funnel from the explosion of the charge in the plan having the configuration of a rectangle

About the authors:

Alexey M. Bubenchikov , Dr. Sci. (Phys.-Math.), Professor, Leading Researcher, Regional Scientific and Educational Mathematical Center, National Research Tomsk State University; bubenchicov_am@mail.ru

Evgeniy B. Brazovskiy , Postgraduate Student, Department of Theoretical Mechanics, National Research Tomsk State University; kondraten.kondraten@mail.ru

Nikita S. Konkov, Associate Professor, I. N. Butakov Scientific and Educational Center, National Research Tomsk Polytechnic University; Deputy Director, Engineering and Technical Center of Gazprom Transgaz Tomsk LLC; n.s.konkov@gmail.com

Abstract:

In this article, using a solid-liquid model of the soil, methods and provisions of the theory of potential flows, as well as the apparatus of analytical functions, an analytical solution to the problem of ejection of soil during an explosion of a charge located on the surface is constructed for the case when this charge has the shape of a rectangle in the plan, whose length far exceeds its width. A distinctive feature of the obtained solution is that within the framework of the formed mathematical model, it is accurate, has a finite form and is expressed in elementary functions.

References:

1.   Bubenchikov A. M., Brazovskiy E. B. 2022. “Hydrodynamic model of a funnel from an explosion of a buried charge”. Tyumen State University Herald. Physical and
Mathematical Modeling. Oil, Gas, Energy, vol. 8, no. 2 (30), pp. 128-141.
DOI: 10.21684/2411-7978-2022-8-2-128-141 [In Russian]

2.    Bubenchikov A. M., Brazovskiy E. B. 2022. “Hydrodynamic model of a funnel from an explosion by a vertically located buried charge”. Explosion Technology, no. 135-92, pp. 94-107. [In Russian]

3.    Viktorov S. D., Zakalinsky V. M., Shipovskii I. E., Mingazov R. Ya. 2021. “The concept of development of drilling and blasting operations in the development of mineral deposits”. Explosion Technology, no. 133-90, pp. 100-112. [In Russian]

4.    Gurevich M. I. Theory of jets of an ideal liquid. Moscow: Fizmatgiz, 1961. 496 p.
[In Russian]

5.    Zakalinsky V. M., Mingazov R. Ya. 2021. “About drilling and blasting operations at large depths”. Explosion Technology, no. 133-90, pp. 113-121. [In Russian]

6.    Kuznetsov V. M. 1977. Mathematical models of explosive business. Novosibirsk: Nauka. Pp. 84-127. [In Russian]

7.    Lavrentiev M. A., Shabat B. V. 1973. Methods of the theory of functions of a complex variable: study guide for universities. 4^th ed., corrected. Moscow: Science. 736 p.
[In Russian]

8.    Milne – Thomson L. M. 1974. Theoretical hydrodynamics. Translated from English by A. A. Petrova et al. Edited by N. N. Moiseeva. Moscow: Mir. 655 p. [In Russian]

9.    Norov A. Yu. 2020. “The problem of controlling the explosion energy during the formation of the collapse of the exploded rock mass in quarries”. Explosion Technology, no. 129-86, pp. 85-104. [In Russian]

10.  Khokhlov S. V., Bazhenova A. V., Makkoev V. A., Rakhmanov R. A., Alenichev I. A. 2021. “Investigation of the issue of management and control over the displacement of ore contours after the blast”. Explosion Technology, no. 132-89, pp. 59-76.
[In Russian]